An FMCW radar and the principle of the prior art are detailed in a range of documents including p. 274ff. of the "Revised Edition Radar Technology" (issued by the Institute for Electronics, Information and Communications Engineers) and "Introduction to Radar Systems" (written by M. I. Skolnik). One improvement in the accuracy of an FMCW radar and its application are also disclosed in Japanese Laid-open Patent No. H5-188141.
An FMCW radar of the prior art is explained next with reference to the drawings. FIG. 2 shows an outline of a first example of a FMCW radar of the prior art. In FIG. 2, the reference numeral 21 is a first distance estimator and the reference numeral 22 is a third velocity estimator.
FIG. 3 shows an outline of a second example of the FMCW radar of the prior art. In FIG. 3, the reference numeral 31 is a first distance estimator, the reference numeral 32 is a first velocity estimator, the reference numeral 33 is a third velocity estimator, the reference numeral 34 is a frequency modulation factor ratio estimator, and the reference 35 is a second distance estimator.
FIGS. 4A and 4B show the relation between the frequency of radio waves to be transmitted or received and time for explaining the principle of the FMCW radar.
Since the specific circuit configuration for obtaining the beat wave in the FMCW radar is not directly associated with the present invention, its explanation is omitted here. An example and block diagram related to such circuit configuration is described in documents including the abovementioned "Introduction to Radar Systems." The frequency of the beat wave is used in the following explanation. Any suitable method may be selected for obtaining the frequency of the beat wave from a range of methods including filter bank and digital signal processing such as FFT after analog-to-digital conversion.
The principle whereby information the distance and velocity is included in the frequency of the beat wave and the method for calculating position and velocity using the FMCW radar of the prior art are explained with reference to FIGS. 4A and 4B.
A wave transmitted by the radar is reflected by a target object (reflector) at a distance R, and returns to the radar after the elapse of time 2R/c (c is the velocity of light).
The emitted wave is a modulated wave whose frequency is modulated with repetitive triangular waves as shown by the bold line in FIG. 4A. Accordingly, the frequency of the returning wave and emitted wave are not equivalent. More specifically, the frequency of signals transmitted, while the emitted wave travels to and back the distance R, is shifted. The beat wave is generated by combining the receiving signal which receives this reflected wave with the transmitted signal, as a result of the difference in the frequencies of these two signals. The frequency of the beat wave f.sub.r can be defined according to the following Equation (1): EQU f.sub.r =(2R/c).times.a (1)
If "a" is the absolute value of the frequency modulation factor which indicates a change in the frequency per unit time, "a" can be defined according to the following Equation (2): EQU a=.vertline.df/dt.vertline. (2)
where "df" is the difference in the frequency modulated vertically using the triangular wave and "dt" is the time spent for sweeping the frequency difference.
When a target object is moving relative to the radar (i.e. when the distance between the radar and target object is changing), the reflected wave causes frequency shifting relative to the incident wave due to the Doppler effect. In other words, the frequency of the reflected wave itself is shifted, and a beat wave is generated which differs from the aforementioned beat wave. The frequency f.sub.v of this beat wave can be defined according to the following Equation (3): EQU f.sub.v =(2V/c).times.f.sub.c ( 3)
where V: relative velocity, and f.sub.c : center frequency of the transmitted wave.
Accordingly, a beat wave which is governed by the distance and velocity defined by Equations (1) and (3) is generated by combining the emitted wave modulated by the triangular wave and the receiving wave which receives reflection of the emitted wave.
A beat frequency f.sub.u during the upward slope of the triangular wave, i.e., while the frequency increases with the elapse of time (hereafter referred to as the upward slope period), can be defined according to the following Equation (4). (Refer to FIG. 4B.) EQU f.sub.u =f.sub.r -f.sub.v ( 4)
On the other hand, the beat frequency f.sub.d during the downward slope of the triangular wave, i.e., while the frequency decreases with the elapse of time (hereafter referred to as the downward slope period), can be defined according to the following Equation (5). (Refer to FIG. 4B.) EQU f.sub.d =f.sub.r +f.sub.v ( 5)
In the FMCW radar of the prior art, the frequencies of the beat wave in each upward and downward slope of frequency modulation by the triangular wave are first calculated. Then, equations (1), (3), (4), and (5) are solved using these values for identifying the relative distance R and the relative velocity V between the radar and target object. Specifically, EQU R=(f.sub.u +f.sub.d)/4/a.times.c (6) EQU V=(f.sub.u -f.sub.d)/4/f.sub.c .times.c (7)
First, the operation of the first example of the FMCW radar of the prior art is explained with reference to FIG. 2. Here, suppose that the absolute value of the modulation factor for the upward slope, the absolute value of the modulation factor for the downward slope, and the absolute value of their mean value which is the average frequency modulation factor are equivalent. The FMCW radar receives respective beat frequencies f.sub.u and f.sub.d during the upward and downward slopes of the frequency modulation from the previous process.
The first distance estimator 21 estimates the relative distance R between the radar and target object in accordance with Equation (6), using the beat frequencies f.sub.u and f.sub.d and an absolute value a of the average frequency modulation factor (the value previously designed or set to the radar based on actual measurement).
The third velocity estimator 22 estimates the relative velocity V between the radar and target object in accordance with Equation (7).
With the above FMCW radar of the prior art and procedures, the distance and velocity are easily identified using the above Equations (6) and (7) based on the beat frequency in the upward and downward slopes of triangular frequency modulation.
Next, the operation of the second example of the FMCW radar of the prior art is explained with reference to FIG. 3. The second example of the FMCW radar of the prior art takes into account the case when an error is included in the absolute value of the frequency modulation factor previously set in the radar. The mean value of absolute values of the frequency modulation factor for the upward and downward slopes is often used as an absolute value of the modulation frequency factor previously set for the radar. Hereafter, this mean value is thus called an absolute value a of the average frequency modulation factor. If the absolute value a is different from an absolute value a.sub.t of the true average frequency modulation factor, the beat frequencies can be defined as follows: EQU f.sub.u =(2R/c).times.a.sub.t -(2V/c).times.f.sub.c ( 8) EQU f.sub.d =(2R/c).times.a.sub.t +(2V/c).times.f.sub.c ( 9)
Here, the first distance estimator 31 calculates the distance using Equation (6). The absolute value a of the frequency modulation factor used in this calculation is a value previously set for the radar. Therefore, the distance R.sub.1 calculated is not the true value. The ratio a/at of the absolute value a of the frequency modulation factor previously set for the radar to the absolute value at of the true frequency modulation factor is called an average frequency modulation factor ratio p. The estimated distance R.sub.1 calculated using Equation (10) is therefore a value multiplying the true distance R by 1/Average frequency modulation factor ratio p. EQU R.sub.1 =R.times.a.sub.t /a=R/p (10)
where P=a/a.sub.t R: true distance.
The first velocity estimator 32 calculates a velocity V.sub.1 from the time difference using the distance calculated by the first distance estimator 31. The velocity V.sub.1 and the true velocity V can be defined according to the following Equation (11): EQU V.sub.1 =V/p (11)
where V: true velocity.
Next, the third velocity estimator 33 calculates the velocity using Equations (8) and (9) as simultaneous equations. The velocity identified using these two equations is the genuine velocity V which is not affected by the absolute value a of the average frequency modulation factor.
Accordingly, the frequency modulation factor ratio estimator 34 calculates the average frequency modulation factor ratio p from the true velocity V calculated by the third velocity estimator 33 and the velocity V.sub.1 calculated by the first velocity estimator 32. Using this p, i.e. by multiplying R.sub.1 by p, the second distance estimator 35 estimates the true R.
With the above configuration, distances and velocities close to their true values may be estimated even if an error exists in the absolute value of the average frequency modulation factor.
However, the FMCW radar with the configuration detailed in the first example may cause an error in the calculated distance and velocity if there is a difference between the actual value and the value previously set for calculating the distance and velocity related to the slope of the average frequency modulation by the triangular wave, i.e., the absolute value of the average frequency modulation factor which is a change in the frequency per unit time.
The FMCW radar with the configuration as detailed in the second example can handle an error in the absolute values of the frequency modulation factor for upward and downward slopes. However, in this radar of the prior art, the absolute values of the frequency modulation factor for the upward slope and downward slopes are supposed to be completely equal as a precondition. If this precondition is not observed, the radar generates a large error in velocity, and the distance may be corrected using the velocity with this large error. Consequently, the aforementioned correction may instead have a detrimental effect.
For example, if the average frequency modulation factor ratio of the previously set absolute value a of the average frequency modulation factor for the upward and downward slopes of the triangular wave to the absolute value au of the true frequency modulation factor for the upward and downward slopes of the triangular wave is other than 1, the distance may deviate by an amount equivalent to the modulation factor ratio. If there is a difference in value between the upward and downward slopes, an error in velocity may be generated in proportion to this difference.